Mathematically precise bisect cuts?
Well, that's not an easy interface to interpret, is it? First, in the top part of the window is &quot;Plane Point&quot; this is a point on the cutting plane. In your case, I think you should set it to the origin (0,0,0). This is also the pivot point for angle adjustments.
The second part of the window is &quot;Plane Normal.&quot; For the Y-Z plane, set it to (1,0,0).   For the X-Z plane, set it to (0, 1, 0) and for the X-Y plane, set it to (0,0,1). In the attached screenshot, it is set to (cos(72°), sin(72°), 0) and the poorly drawn white arcs show 72° for the normal referenced from the x-axis and 72° for the cutter plane referenced from the y-axis.
To further expand, lets cut out Suzanne's face at +/1 36°. I put sin(36°) and cos(36°) into a calculator and got 0.588 and 0.809 so lets see how to put those in: